1. Field of the Invention
This invention relates to multistage hydraulic machines operable as pumps or turbines. More specifically, this invention relates to a reversible two-stage pump/turbine for a hydraulic installation having an operating head generally in excess of 1,000 meters.
2. Description of the Prior Art
In the art, hydraulic pumped storage facilities are well known for storing energy during periods of low electrical demand by pumping water from a low elevation reservoir to a high elevation reservoir. During periods of peak electrical demand, the stored energy is released by passing the water from the upper reservoir through a hydraulic turbine to the lower reservoir. The turbine converts the stored energy, or potential energy, into electrical energy by driving a generator. The potential energy is proportional to the difference in elevation between the upper and lower reservoirs (commonly, referred to as the operating head).
Historically, pumped storage facilities employed separate pumps and hydraulic turbines of conventional design. With the development of reversible pump/turbines, a single machine could perform both the pumping and generating operations. Originally, reversible pump/turbines were provided with a single stage. That is, a single runner, commonly a Francis-type runner, was mounted on a rotary shaft with the shaft engaging a motor/generator. In pumping operation, the shaft is driven by the motor with the runner creating a pressure head for pumping water to the higher reservoir. In the turbine mode, water flowing through the runner to the lower reservoir would cause the shaft to rotate and the associated generator would produce the desired electrical power.
Single-stage pump/turbines are designed such that, when operated in the turbine mode, water approaching the runner from the upper reservoir will be provided with a whirl. The whirl is formed by a spiral case and fixed vanes which are typically provided around the runner's circumference. Due to the whirl, the water has a circumferential velocity component in the shaft rotation and approaches the runner in spiral paths. The whirl is removed by the runner causing the desired rotation of the shaft.
At high efficiency, the water leaves the runner of a single-stage pump/turbine with little appreciable whirl. The change in whirl is related to the operating head and angular velocity of the shaft by the following equation, generally referred to as Euler's equation: EQU V.sub.u1 R.sub.1 -V.sub.u2 R.sub.2 =g(He/W)
where V.sub.u1 R.sub.1 and V.sub.u2 R.sub.2 are the values of whirl of the water approaching and leaving the runner, respectively. V.sub.u1 and V.sub.u2 represent the circumferential components of water velocity approaching and leaving the runner, respectively, with R.sub.1 and R.sub.2 representing the radii (measured perpendicularly from the shaft's axis of rotation) of the runner's entrance and exit. The values g, H, e and W respectively refer to the acceleration of gravity, the operating head, the hydraulic efficiency, and the angular velocity of the turbine shaft. For modern single-stage turbine installations, hydraulic efficiency (e) is generally in excess of 90% with the value of whirl exiting the runner being small in comparison with the value of whirl approaching the runner.
As can be seen from Euler's equation, the value of whirl approaching the runner (V.sub.u1 R.sub.1) is almost directly proportional to the operating head (H) when the value of V.sub.u2 R.sub.2 is very small. Accordingly, for very high head installations (for example, installations having operating heads in excess of 1,000 meters), the value of whirl approaching the runner (V.sub.u1 R.sub.1) becomes so large that the relative velocity of the water (expressed W.sub.u1 =V.sub.u1 -WR.sub.1) becomes positive and is directed toward the shaft rotation. The relative velocity at the outlet of the runner (W.sub.u1 =V.sub.u2 -WR.sub.2) is always negative since the value of V.sub.u2 R.sub.2 is very small. This relationship between the values W.sub.u1 and W.sub.u2 results in an extremely curved shape of the runner blade which leads to lower values of efficiency.
To overcome the problems associated with positive relative velocity, multistage pump/turbines were developed for high head installations. A conventional two-stage pump/turbine is provided with two Francis-type runners arranged in series on a common shaft. An example of such a two-stage pump/turbine is shown in U.S. Pat. No. 4,280,788 to Tsunoda et al dated July 28, 1981. As shown in Tsunoda, when the machine is operated in the turbine mode, water is delivered to the radial openings of a first-stage, or high pressure, Francis-type runner and discharged from the runner in an axial direction. A return passage directs the water discharged from the first-stage runner to radial openings of a second-stage, or low pressure, Francis-type runner. Discharge from the second-stage runner is also in the axial direction.
Under the arrangement as shown in Tsunoda, the potential energy represented by the operating head is divided between the two runners by design of stay vanes and control of wicket gates in the first stage to reduce the value of whirl of the water delivered to the first-stage runner. The whirl is so reduced such that the relative velocity of the water is maintained at a negative value. As the water passes through the first-stage runner, the whirl is taken out of the water by the runner for driving the turbine shaft. The water discharges from the first-stage runner with a small value of whirl and is directed through the return passage to the second-stage runner. Stay vanes or wicket gates surrounding the second-stage runner impart to the water a value of whirl as it approaches the second-stage runner. The second-stage runner removes this whirl and discharges the water with little appreciable whirl. In both the first and second stages, the water is directed toward the runners in spiral paths having rotational directions in common with the rotational direction of the shaft. For convenience, a whirl in a direction in common with the shaft rotation may be referred to as a positive whirl while a whirl in a direction opposite to the shaft rotation may be referred to as a negative whirl. The arithmetic sum of the whirls removed by the first and second-stage runners is proportional to the operating head.
While conventional two-stage pump/turbines, as described, are effective for avoiding problems of positive relative water velocity while efficiently converting potential energy into kinetic energy by dividing the potential energy between two runners, certain problems are associated with such pump/turbines. First, the need for a return passage requires the first and second-stage runners to be materially spaced apart on the shaft which increases the length of the shaft resulting in increased weight and costs. Second, while such pump/turbine are regulatable in the turbine mode (by adjustable wicket gates), they are not regulatable in the pump mode. Third, either the shaft is long and directed by a bearing embedded in a draft tube (as shown in Tsunoda) or the shaft terminates with the second-stage runner with no guide bearing in the second stage. In either case, the pump/turbine is subject to critical speed limitations.